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Popular >

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

Solution

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

Solution

y = c_{1} e^{4 t} + c_{2} - \frac{t}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} - \frac{t}{4}

y = c_{1} e^{4 t} + c_{2} - \frac{t}{4}

Graph

Popular Examples

y^{''}+5y=e^{2x}-x-x^2+x^3

y^{^{''}} + 5 y = e^{2 x} - x - x^{2} + x^{3}

y^{'''}-5y^{''}+6y^'=6e^x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{x}

y^{''}-2y^'+2y=cos^2(x)

y^{^{''}} - 2 y^{^{'}} + 2 y = cos^{2} (x)

1/8 x^{''}+x^'+2x=12.5*sin(2t)

\frac{1}{8} x^{^{''}} + x^{^{'}} + 2 x = 12.5 \cdot sin (2 t)

y^{''}+y=(sin(x))/((cos(x))^2)

y^{^{''}} + y = \frac{sin ( x )}{( cos ( x ) ) ^{2}}

Frequently Asked Questions (FAQ)

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