What is the solution for y^{''}+4*y=3*x-1 ?

The solution for y^{''}+4*y=3*x-1 is y=c_{1}cos(2x)+c_{2}sin(2x)+(3x)/4-1/4

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y^{''}+4y=3x-1

y^{^{''}} + 4 \cdot y = 3 \cdot x - 1

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{3 x}{4} - \frac{1}{4}

Solution steps

y^{''} (x) + 4 \cdot y = 3 \cdot x - 1

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{3 x}{4} - \frac{1}{4}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{3 x}{4} - \frac{1}{4}

\int_{0}^{0.5} 625 x d x

f (x) = x 3^{x}

(sin^{2} (3 x))^{^{'}}

\int \frac{5 - 50 x}{9 - 25 x ^{2}} d x

What is the solution for y^{''}+4*y=3*x-1 ?
The solution for y^{''}+4*y=3*x-1 is y=c_{1}cos(2x)+c_{2}sin(2x)+(3x)/4-1/4