7.3.25 problem 25

Internal problem ID [65]
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 : 25
Date solved : Friday, February 07, 2025 at 07:47:34 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-y&=2 y x^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

dsolve([x*diff(y(x),x)-y(x)= 2*x^2*y(x),y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 14

DSolve[{x*D[y[x],x]-y[x]== 2*x^2*y[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2-1} x \]