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Popular >

4y^{''}-y=1

Solution

4 y^{^{''}} - y = 1

Solution

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- \frac{t}{2}} - 1

Solution steps

4 y^{''} (t) - y = 1

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- \frac{t}{2}} - 1

y = c_{1} e^{\frac{t}{2}} + c_{2} e^{- \frac{t}{2}} - 1

Popular Examples

integral of sqrt(e^{3x)}

\int e^{3 x} d x

tangent of (x^2-9)^2 tangent of

(x^{2} - 9)^{2}

y^{''}-3y^'-10y=4,y(0)=0,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} - 10 y = 4, y (0) = 0, y^{^{'}} (0) = 0

integral from 1 to e^7 of (ln^2(x^2))/x

\int_{1}^{e^{7}} \frac{ln ^{2} ( x ^{2} )}{x} d x

sum from n=1 to infinity of (3/n)^4

n = 1 \sum \infty (\frac{3}{n})^{4}

Frequently Asked Questions (FAQ)

What is the solution for 4y^{''}-y=1 ?
The solution for 4y^{''}-y=1 is y=c_{1}e^{t/2}+c_{2}e^{-t/2}-1