4.4 problem 4

Internal problem ID [57]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 4.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {-2 y x +y^{\prime }-{\mathrm e}^{x^{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 12

dsolve(-2*x*y(x)+diff(y(x),x) = exp(x^2),y(x), singsol=all)
 

\[ y \relax (x ) = \left (c_{1}+x \right ) {\mathrm e}^{x^{2}} \]

Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 15

DSolve[-2*x*y[x]+y'[x] == Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{x^2} (x+c_1) \\ \end{align*}