Solve the differential equation? 2dy/dx-y=e^x/2 .

1 Answer
Jun 10, 2018

y=1/2xe^(x/2)+Ce^(x/2)y=12xex2+Cex2

Explanation:

2(dy)/(dx)-y=e^(x/2)2dydxy=ex2

=>(dy)/(dx)+(-1/2)y=1/2e^(x/2)--(1)dydx+(12)y=12ex2(1)

Integrating factor

e^(-(1/2)intdx)=e^(-x/2)e(12)dx=ex2

multiply (1)(1) by e^(-x/2)ex2

e^(-x/2)(dy)/(dx)-1/2e^(-x/2)y=1/2ex2dydx12ex2y=12

=>d/(dx)(ye^(-1/2x))=1/2ddx(ye12x)=12

integrating

ye^(-1/2x)=1/2x+Cye12x=12x+C

':.y=1/2xe^(x/2)+Ce^(x/2)