71.4.20 problem 20

Internal problem ID [14392]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 06:29:27 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 2.333 (sec). Leaf size: 44

dsolve([diff(y(x),x)=y(x)/(4-x^2)+sqrt(x),y(3) = 4],y(x), singsol=all)
 

\[ y = \frac {\left (4 \,5^{{3}/{4}}+5 \left (\int _{3}^{x}\frac {\sqrt {\textit {\_z1}}\, \left (\textit {\_z1} -2\right )^{{1}/{4}}}{\left (\textit {\_z1} +2\right )^{{1}/{4}}}d \textit {\_z1} \right )\right ) \left (x +2\right )^{{1}/{4}}}{5 \left (x -2\right )^{{1}/{4}}} \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 63

DSolve[{D[y[x],x]==y[x]/(4-x^2)+Sqrt[x],{y[3]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _3^x\frac {1}{4-K[1]^2}dK[1]\right ) \left (\int _3^x\exp \left (-\int _3^{K[2]}\frac {1}{4-K[1]^2}dK[1]\right ) \sqrt {K[2]}dK[2]+4\right ) \]