Internal problem ID [878]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 4(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-x \sin \left (x^{2}\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 12
dsolve([diff(y(x),x) = x*sin(x^2),y(1/2*2^(1/2)*Pi^(1/2)) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\cos \left (x^{2}\right )}{2}+1 \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 15
DSolve[{y'[x] == x*Sin[x^2],y[Sqrt[Pi/2]]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1-\frac {\cos \left (x^2\right )}{2} \\ \end{align*}