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Differential Equation Calculator

Solve differential equations

The calculator will try to find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous.

Initial conditions are also supported.

Enter an equation (and, optionally, the initial conditions):
For example, y''(x)+25y(x)=0, y(0)=1, y'(0)=2.
Write `y'(x)` instead of `(dy)/(dx)`, `y''(x)` instead of `(d^2y)/(dx^2)`, etc.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your input: solve $$$2 x y{\left(x \right)} + y ' \left(x \right) = x$$$

Answer

$$$y{\left(x \right)} = \frac{C_{1} e^{- x^{2}}}{2} + \frac{1}{2}$$$