Internal problem ID [75]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {-2 y x +y^{\prime }=3 x^{2} {\mathrm e}^{x^{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(y(x),x) = 3*exp(x^2)*x^2+2*x*y(x),y(0) = 5],y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{3}+5\right ) {\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 16
DSolve[{y'[x] == 3*Exp[x^2]*x^2+2*x*y[x],y[0]==5},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x^2} \left (x^3+5\right ) \]