71.7.5 problem 5

Internal problem ID [14426]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 06:30:39 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 17

dsolve([diff(y(x),x)=y(x)/x+sin(x^2),y(-1) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 20

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

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