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Popular Calculus >

y^{''}+y=xcos^3(x)

Solution

y^{^{''}} + y = x cos^{3} (x)

Solution

y = c_{1} cos (x) + c_{2} sin (x) + \frac{24 x ^{2} sin ( x ) + 32 x cos ^{5} ( x ) - 12 x cos ( x ) - 12 x sin ( x ) sin ( 4 x ) + 128 x cos ^{3} ( x ) sin ^{2} ( x ) + 3 cos ( x ) sin ( 4 x ) - 3 sin ( x ) cos ( 4 x )}{128}

Solution steps

y^{''} (x) + y = x cos^{3} (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{24 x ^{2} sin ( x ) + 32 x cos ^{5} ( x ) - 12 x cos ( x ) - 12 x sin ( x ) sin ( 4 x ) + 128 x cos ^{3} ( x ) sin ^{2} ( x ) + 3 cos ( x ) sin ( 4 x ) - 3 sin ( x ) cos ( 4 x )}{128}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{24 x ^{2} sin ( x ) + 32 x cos ^{5} ( x ) - 12 x cos ( x ) - 12 x sin ( x ) sin ( 4 x ) + 128 x cos ^{3} ( x ) sin ^{2} ( x ) + 3 cos ( x ) sin ( 4 x ) - 3 sin ( x ) cos ( 4 x )}{128}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y=xcos^3(x) ?
The solution for y^{''}+y=xcos^3(x) is