25.1.15 problem 15

Internal problem ID [4227]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 15
Date solved : Monday, January 27, 2025 at 08:43:03 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 12

dsolve([diff(y(x),x)-2*x*y(x)=2*x,y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 14

DSolve[{D[y[x],x]-2*x*y[x]==2*x,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

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