What is the solution for y^{''}+y=4x+10sin(x),y(pi)=0,y^'(pi)=2 ?

The solution for y^{''}+y=4x+10sin(x),y(pi)=0,y^'(pi)=2 is y=9picos(x)+7sin(x)+4x-5xcos(x)

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y^{''}+y=4x+10sin(x),y(pi)=0,y^'(pi)=2

y^{^{''}} + y = 4 x + 10 sin (x), y (π) = 0, y^{^{'}} (π) = 2

y = 9 π cos (x) + 7 sin (x) + 4 x - 5 x cos (x)

Solution steps

y^{''} (x) + y = 4 x + 10 sin (x)

Solve linear ODE:

y = 9 π cos (x) + 7 sin (x) + 4 x - 5 x cos (x)

y = 9 π cos (x) + 7 sin (x) + 4 x - 5 x cos (x)

9 y^{^{''}} - 6 y^{^{'}} + y = cos (t)

y^{^{''}} - 9 y = x + 2

y^{^{''}} - y = c^{x} + 2 c^{2 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = x e^{2 x} + x^{3} e^{2 x}

y^{^{''}} - 11 y^{^{'}} + 10 y = 2 x^{2} - 44 x + 4

What is the solution for y^{''}+y=4x+10sin(x),y(pi)=0,y^'(pi)=2 ?
The solution for y^{''}+y=4x+10sin(x),y(pi)=0,y^'(pi)=2 is y=9picos(x)+7sin(x)+4x-5xcos(x)