Problem 03 | Equations with Homogeneous Coefficients Problem 03 2(2x2+y2)dx−xydy=0 Solution 03 2(2x2+y2)dx−xydy=0 Let y=vx dy=vdx+xdv 2(2x2+v2x2)dx−vx2(vdx+xdv)=0 4x2dx+2v2x2dx−v2x2dx−vx3dv=0 4x2dx+v2x2dx−vx3dv=0 x2(4+v2)dx−vx3dv=0 x2(4+v2)dxx3(4+v2)−vx3dvx3(4+v2)=0 dxx−vdv4+v2=0 Read more about Problem 03 | Equations with Homogeneous CoefficientsLog in or register to post comments
Problem 02 | Equations with Homogeneous Coefficients Problem 02 (x−2y)dx+(2x+y)dy=0 Solution 02 (x−2y)dx+(2x+y)dy=0 Let y=vx dy=vdx+xdv Substitute, (x−2vx)dx+(2x+vx)(vdx+xdv)=0 xdx−2vxdx+2vxdx+2x2dv+v2xdx+vx2dv=0 xdx+2x2dv+v2xdx+vx2dv=0 (xdx+v2xdx)+(2x2dv+vx2dv)=0 x(1+v2)dx+x2(2+v)dv=0 Read more about Problem 02 | Equations with Homogeneous CoefficientsLog in or register to post comments
Problem 01 | Equations with Homogeneous Coefficients Problem 01 3(3x2+y2)dx−2xydy=0 Solution 01 3(3x2+y2)dx−2xydy=0 Let y=vx dy=vdx+xdv Substitute, 3(3x2+v2x2)dx−2vx2(vdx+xdv)=0 3(3+v2)x2dx−2vx2(vdx+xdv)=0 Divide by x2, 3(3+v2)dx−2v(vdx+xdv)=0 9dx+3v2dx−2v2dx−2vxdv=0 9dx+v2dx−2vxdv=0 (9+v2)dx−2vxdv=0 Read more about Problem 01 | Equations with Homogeneous CoefficientsLog in or register to post comments