8.3.24 problem 25

Internal problem ID [700]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:58:26 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

dsolve([-y(x)+x*diff(y(x),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: 0.029 (sec). Leaf size: 14

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

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