8.3.21 problem 22

Internal problem ID [697]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 22
Date solved : Wednesday, February 05, 2025 at 03:56:53 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-y+4 x^{3} y \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve([diff(y(x),x) = -y(x)+4*x^3*y(x),y(1) = -3],y(x), singsol=all)
 

\[ y = -3 \,{\mathrm e}^{x \left (x -1\right ) \left (x^{2}+x +1\right )} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 16

DSolve[{D[y[x],x]== -y[x]+4*x^3*y[x],y[1]==-3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -3 e^{x^4-x} \]