Internal problem ID [47]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+y-4 y x^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 18
dsolve([diff(y(x),x) = -y(x)+4*x^3*y(x),y(1) = -3],y(x), singsol=all)
\[ y \relax (x ) = -3 \,{\mathrm e}^{x \left (x -1\right ) \left (x^{2}+x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 16
DSolve[{y'[x]== -y[x]+4*x^3*y[x],y[1]==-3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -3 e^{x^4-x} \\ \end{align*}