m32352_10

1. xyy = 1x².

2. y(e^x+1)dye^xdx = 0.

3. xyy= 2xlnx; y(1)=1.

4. ycos²x+y = (2+x²)e^tgxcos²x;

y(0)=1.

5. y+2y+10y =0;

y()=0, y()=1.

6. y8y+15y = 0;

y(0)=1, y(0)= 2.

7. y5y+6y = 2xe^x.

8. y+4y = 5sin3x.

1.

2. (e^x+2)y = ye^x.

3. x³y+3x²y = 2; y(1)=2.

4. y+3x²y = x³ ; y(0)=1.

5. y6y+9y =0;

y(0)=1, y(0)=0.

6. y2y = 0;

y(1)=0, y(1)=2.

7. y+8y = (x1)e^2x.

8. y2y3y = x²3x+2.

1. xydx+(x+1)dy = 0.

2. y = e^2x3y.

3. y+y = (x+1)e^x; y(0)=1.

4. xy y = x²cos3x; y()=1.

5. y+8y+7y = 0;

y(0)=2, y(0)=1.

6. y+y = 0;

y()= 1, y()= 4.

7. y6y+8y = 2sin3x.

8. y+2y+3y = 5e^4x.

1. 2x²yy+y² = 2.

2. xydy = (3x²+2 1)dx.

3. xy+y = x+1; y(1)=2.

4. ysin²x+y = 4x³e^ctgxsin²x;

y()=0.

5. y+9y = 0;

y()=0, y()=1.

6. y7y+6y = 0;

y(0)=2, y(0)=0.

7. y2y3y = 3x²+2x1.

8. y4y+4y = 2cos3x.

1. y = (y²+1)tgx.

2. cos²2xdy dx = 0.

3. yycosx = cosx; y(0)=1.

4. (1+x²) y+y = (1+x)e^arctgx;

y(0)=1.

5. y7y+12y =0;

y(0)=2, y(0)= 2.

6. y+8y+16y = 0;

y(0)=1, y(0)=0.

7. y+y2y =2e^5x.

8. y+5y = 3x²2.

1. x(1+y²)dx+y dy = 0.

2. y² y = y³+2.

3. xyy = xlnx; y(1)=2.

4. y+ytgx = cos^1x; y(0)=0.

5. y+9y =0;

y(0)=1, y(0)= 3.

6. y6y+9y = 0;

y(0)=1, y(0)=2.

7. y+6y = 2e^2x.

8. y+2y8y = 3cos4x.

1. xydx+(1+y²) dy = 0.

2. ycos3xy²sin3x = 0.

3. y 4 = 4x³; y(1)=2.

4. ycosx+ysinx = 1; y(0)=1.

5. y3y+2y = 0;

y(0)=0, y(0)=1.

6. y8y+16y = 0;

y(0)=2, y(0)=5.

7. y+7y = 5x²+x3.

8. y3y+2y = 2cosx.

1. xyy² = 1.

2. (e^x 1)dy+e^x dx = 0.

3. xy+3y = 2x³; y(1)=3.

4. yysinx = e^cosx sin2x; y(0)=1.

5. y5y+6y = 0;

y(0)=5, y(0)=0.

6. y4y+13y = 0;

y()=0, y()=1.

7. yy = 3e^2x.

8. y2y+y = x²+1.

1. ycosx (y+2)sinx = 0.

2. x²lnydy+(1+x)ydx = 0.

3. y+ = 1+x³; y(1)=1.

4. y+2xy = 2x ; y(0)=2.

5. y2y+5y = 0;

y(0)= 1, y(0)=0.

6. y+y2y = 0;

y(0)= 4, y(0)= 1.

7. y+3y10y = 2sin5x.

8. y+2y+y = 3e^3x.

1. y (y²+3)ctgx = 0.

2. (y²+2) dyydx = 0.

3. y+2xy = 3x² ; y(0)=2.

4. y+y = ; y(0)=2.

5. y+16y = 0;

y()= 1, y()=0.

6. y4y = 0;

y(0)=2, y(0)= 3.

7. y+2y = 2x²5.

8. y6y+9y = cos2x.

1. ycos²xylny = 0.

2.y=2^3x+5y.

3. xyy = 2x³; y(1)=1.

4. (1+x²)y2xy = (1+x²)²;

y(0)=1.

5. y+10y+25y = 0;

y(0)=1, y(0)= 1.

6. y4y+3y = 0;

y(0)=1, y(0)=3.

7. y5y24y = 5e^6x.

8. y4y+5y = 2x²+x4.

1. ycos²3x = 2y².

2. (e^2x+1)dy+ye^2xdx = 0.

3. xy+2x²y = lnx; y(1)=1.

4. xy3y = x⁴; y(1)=1.

5. y6y = 0;

y(0)=2, y(0)= 2.

6. y+2y+5y = 0;

y(0)=1, y(0)=1.

7. y2y3y = 8cos2x.

8. y4y+4y = 3e^5x.

1. xyy = (1x²)(1+y²).

2. y(2+x)dy (2y²)dx = 0.

3. yyctgx = ; y()=1.

4. xy+2y = ; y(1)=1.

5. y4y+4y =0; y(0)=1, y(0)=3.

6. y+6y = 0; y(0)=0, y(0)=1.

7. y+2y3y = 3x².

8. y+4y = 3sin3x.

1. x²dy+(y²+2)dx = 0.

2. ylnyy(2x1) = 0.

3. xyy = x²sin2x; y()=1.

4. ycosx2ysinx = 2; y(0)=1.

5. y4y+17y = 0;

y(0)=2, y(0)=1.

6. y+9y = 0;

y(0)=1, y(0)=3.

7. y+8y+16y = 3e^2x.

8. y+2y+10y = sin2x.

1. y(e^x+1)dye^xdx = 0.

2. y²dy+(1 ) dx = 0.

3. ycos²x+y = (2x²)e^tgxcos²x;

y(0)=1.

4. y 4xy = x; y(1)=2.

5. y8y+15y = 0;

y(0)=1, y(0)= 2.

6. y+2y+y = 0;

y(0)=2, y(0)=2.

7. y+4y = 5sin3x.

8. y+y6y = x²1.

1. (e^x+2)y = ye^x.

2. xy2y1 = y².

3. y+3x²y = x³ ; y(0)=1.

4. xyy = x³; y(1)=0.

5. y2y = 0;

y(1)=0, y(1)=2.

6. y10y+25y = 0;

y(0)=2, y(0)= 1.

7. y2y3y = x²3x+2.

8. y+9y = 4e^2x.

1. xyy = 1x².

2. ycos²3x = 2y².

3. xyy = 2xlnx; y(1)=1.

4. (1+x²)y2xy = (1+x²)²; y(0)=1.

5. y+2y+10y =0;

y()=0, y()=1.

6. y6y = 0;

y(0)=2, y(0)= 2.

7. y5y+6y = 2xe^x.

8. y2y+y = 8cos2x.

1.

2. ycos²xylny = 0.

3. x³y+3x²y = 2; y(1)=2.

4. xyy = 2x³; y(1)=1.

5. y6y+9y =0;

y(0)=1, y(0)=0.

6. y+3y+2y = 0;

y(0)=1, y(0)= 1.

7. y+8y = (x1)e^2x.

8. y5y24y = 5sin6x.

1. xydx+(x+1)dy = 0.

2. y (y²+3)ctgx = 0.

3. y+y = (x+1)e^x; y(0)=1.

4. yysinx = e^cosx sin2x;

y(0)=1.

5. y+8y+7y = 0;

y(0)=2, y(0)=1.

6. y16y = 0;

y()= 1, y()=0.

7. y6y+9y = 2sin4x.

8. y+2y = 2x²5.

1. 2x²yy+y² = 2.

2. ycosx (y+2)sinx = 0.

3. xy+y = x+1; y(1)=2.

4. y+2xy = 2x ; y(0)=2.

5. y+9y = 0;

y()=0, y()=1.

6. y2y+5y = 0;

y(0)= 1, y(0)=0.

7. y2y3y = 3x²+2x1.

8. y+6y+9y = 2sin5x.

1. y = (y²+1)tgx.

2. xyy² = 1.

3. yycosx = cosx; y(0)=1.

4. xy+3y = 2x³; y(1)=3.

5. y7y+12y =0;

y(0)=2, y(0)= 2.

6. y+5y = 0;

y(0)=5, y(0)=0.

7. y4y+4y =2e^5x.

8. yy = 2sin3x4cos3x.

1. x(1+y²)dx+y dy = 0.

2. ycos3xy²sin3x = 0.

3. xyy = xlnx; y(1)=2.

4. y4 = 4x³; y(1)=2.

5. y+9y =0; y(0)=1,

y(0)= 3.

6. y3y+2y = 0;

y(0)=0, y(0)=1.

7. y+6y = 2e^2x.

8. y+8y+16y = 5x²+x3.

1. x(1+y²)dx+y dy = 0.

2. (e^x+2)y = ye^x.

3. xyy = xlnx; y(1)=2.

4. y+3x²y = x³ ; y(0)=1.

5. y+9y =0;

y(0)=1, y(0)= 3.

6. y2y+y = 0;

y(0)=0, y(0)=2.

7. y+6y = 2e^2x.

8. y+4y+3y = 5sin3x.

1. cos²2xdy dx = 0.

2. ycos²xylny = 0.

4. (1+x²) y+y = (1+x)e^arctgx;

y(0)=1.

4. xyy = 2x³; y(1)=1.

5. y+8y+16y = 0;

y(0)=1, y(0)=0.

6. y+3y+2y = 0;

y(0)=1, y(0)= 1.

7. y+5y = 3x²2.

8. y5y24y = 5sin6x.

1. xydy = (3x²+2 1)dx.

2. ycosx (y+2)sinx = 0.

3. ysin²x+y = 4x³e^ctgxsin²x;

y()=0.

4. y+2xy = 2x ; y(0)=2.

5. y7y+6y = 0;

y(0)=2, y(0)=0.

6. y2y+5y = 0;

y(0)= 1, y(0)=0.

7. y4y+4y = 2cos3x.

8. y+6y+8y = 2e^3x.

1. y = e^2x3y.

2. x(1+y²)dx+y dy = 0.

3. xyy = x²cos3x; y()=1.

4. xyy = xlnx; y(1)=2.

5. y+y = 0;

y()= 1, y()= 4.

6. y3y+2y = 0;

y(0)=0, y(0)=1.

7. y+2y+3y = 5e^4x.

8. y+8y+16y = 5x²+x3.

1. x²dy+(y²+2)dx = 0.

2. y(e^x+1)dye^xdx = 0.

3. xyy = x²sin2x; y()=1.

4. ycos²x+y = (2+x²)e^tgxcos²x; y(0)=1.

5. y4y+3y = 0;

y()=0, y()=1.

6. y8y+15y = 0;

y(0)=1, y(0)= 2.

7. y+8y+16y = 3e^2x.

8. y+4y = 5sin3x.