What is the solution for (dy)/(dx)+x^2y=10x^2,y(1)=5 ?

The solution for (dy)/(dx)+x^2y=10x^2,y(1)=5 is y=10-5e^{(1-x^3)/3}

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(dy)/(dx)+x^2y=10x^2,y(1)=5

\frac{d y}{d x} + x^{2} y = 10 x^{2}, y (1) = 5

y = 10 - 5 e^{\frac{1 - x ^{3}}{3}}

Solution steps

\frac{d y}{d x} + x^{2} y = 10 x^{2}

Solve linear ODE:

y = 10 - 5 e^{\frac{1 - x ^{3}}{3}}

y = 10 - 5 e^{\frac{1 - x ^{3}}{3}}

\int_{- \infty}^{0} \frac{1}{5 - 2 x} d x

\frac{3 x}{7 x ^{2} + 1}

n = 1 \sum \infty \frac{5}{6 n + 4}

\frac{\partial}{\partial x} (16 - x^{2})

f (x) = \frac{cos ( x )}{2 + sin ( x )}

What is the solution for (dy)/(dx)+x^2y=10x^2,y(1)=5 ?
The solution for (dy)/(dx)+x^2y=10x^2,y(1)=5 is y=10-5e^{(1-x^3)/3}