12.1.10 problem 4(b)

Internal problem ID [1528]
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)
Date solved : Monday, January 27, 2025 at 04:58:56 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x \sin \left (x^{2}\right ) \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = -\frac {\cos \left (x^{2}\right )}{2}+1 \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 15

DSolve[{D[y[x],x] == x*Sin[x^2],y[Sqrt[Pi/2]]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 1-\frac {\cos \left (x^2\right )}{2} \]