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.
Your input: solve $$$y^{2}{\left(x \right)} y ' \left(x \right) = 3 x^{2} + 5$$$
Answer
$$$y{\left(x \right)} = \frac{\left(- \sqrt[3]{3} - 3^{\frac{5}{6}} i\right) \sqrt[3]{C_{1} + x^{3} + 5 x}}{2}$$$
$$$y{\left(x \right)} = \frac{\left(- \sqrt[3]{3} + 3^{\frac{5}{6}} i\right) \sqrt[3]{C_{1} + x^{3} + 5 x}}{2}$$$
$$$y{\left(x \right)} = \sqrt[3]{C_{1} + 3 x^{3} + 15 x}$$$