65.4.21 problem 21

Internal problem ID [15680]
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 : 21
Date solved : Thursday, October 02, 2025 at 10:22:58 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.081 (sec). Leaf size: 47

ode:=diff(y(x),x) = y(x)/(-x^2+4)+x^(1/2); 
ic:=[y(1) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 63

ode=D[y[x],x]==y[x]/(4-x^2)+Sqrt[x]; 
ic={y[1]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {1}{4-K[1]^2}dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\frac {1}{4-K[1]^2}dK[1]\right ) \sqrt {K[2]}dK[2]-3\right ) \end{align*}

✓ Sympy. Time used: 138.375 (sec). Leaf size: 570

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x) + Derivative(y(x), x) - y(x)/(4 - x**2),0) 
ics = {y(1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]