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Popular >

y^'+t*y=y,y(1)=3

Solution

y^{^{'}} + t \cdot y = y, y (1) = 3

Solution

y = 3 e^{t + \frac{- t ^{2} - 1}{2}}

Solution steps

y^{'} (t) + t \cdot y = y

Solve separable ODE:

y = 3 e^{t + \frac{- t ^{2} - 1}{2}}

y = 3 e^{t + \frac{- t ^{2} - 1}{2}}

Graph

Popular Examples

y^'=2y+3,y(0)=5

y^{^{'}} = 2 y + 3, y (0) = 5

((dy}{dx})=\frac{2y)/x

(\frac{d y}{d x}) = \frac{2 y}{x}

(dy}{dt}=\frac{sin^2(t)+t)/y

\frac{d y}{d t} = \frac{sin ^{2} ( t ) + t}{y}

2 (x - 1) y^{^{'}} - 3 y = 0

y^'(x)=(x^2)/(1-y^2),y(2)=3

y^{^{'}} (x) = \frac{x ^{2}}{1 - y ^{2}}, y (2) = 3

Frequently Asked Questions (FAQ)

What is the solution for y^'+t*y=y,y(1)=3 ?
The solution for y^'+t*y=y,y(1)=3 is y=3e^{t+(-t^2-1)/2}