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  • If y1 (x) is solution of the differential equation dy/dx - f(x) y=0 , then a solution of the differential equation dy/dx +f(x) y= r(x) is

If y1 (x) is solution of the differential equation dy/dx - f(x) y=0 , then a solution of the differential equation dy/dx +f(x) y= r(x) is

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Solution:  

              fracmathrmd ymathrmd x-f(x)y=0

       herefore      fracdyy=f(x)dxRightarrow int fracdyy=int f(x)dx

      Rightarrow        y_1(x)=e^int f(x)dx.

       Then for given  equation  ,   I.F=e^int f(x)dx

      Hence , solution  is   ycdot y_1(x)=int r(x)cdot y_1(x)dx hspace0.2cm+c

     Rightarrow        y=frac1y_1(x)int r(x)cdot y_1(x)dx hspace0.2cm+fraccy_1(x)

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Deependra Verma

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