7.3.22 problem 22

Internal problem ID [62]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 22
Date solved : Friday, February 07, 2025 at 07:47:28 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 18

dsolve([diff(y(x),x)= 4*x^3*y(x)-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]== 4*x^3*y[x]-y[x],{y[1]==-3}},y[x],x,IncludeSingularSolutions -> True]
 

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