67.1.4 problem 2.2 (d)

Internal problem ID [16269]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (d)
Date solved : Thursday, October 02, 2025 at 10:45:09 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 83

ode:=x*diff(y(x),x) = arcsin(x^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {i \arcsin \left (x^{2}\right )^{2}}{4}+\frac {\arcsin \left (x^{2}\right ) \ln \left (1-i x^{2}-\sqrt {-x^{4}+1}\right )}{2}+\frac {\arcsin \left (x^{2}\right ) \ln \left (1+i x^{2}+\sqrt {-x^{4}+1}\right )}{2}-\frac {i \operatorname {polylog}\left (2, \left (i x^{2}+\sqrt {-x^{4}+1}\right )^{2}\right )}{4}+c_1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 25

ode=x*D[y[x],x]==ArcSin[x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\frac {\arcsin \left (K[1]^2\right )}{K[1]}dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 3.207 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - asin(x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \int \frac {\operatorname {asin}{\left (x^{2} \right )}}{x}\, dx \]