85.33.79 problem 80

Internal problem ID [22702]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 80
Date solved : Thursday, October 02, 2025 at 09:11:05 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 50

ode:=(x^3+1)^(1/2)*diff(y(x),x) = x^2*y(x)+x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\int \frac {x^{2} {\mathrm e}^{-\int \frac {x^{2}}{\sqrt {x^{3}+1}}d x}}{\sqrt {x^{3}+1}}d x +c_1 \right ) {\mathrm e}^{\int \frac {x^{2}}{\sqrt {x^{3}+1}}d x} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to -1+c_1 e^{\frac {2 \sqrt {x^3+1}}{3}}\\ y(x)&\to -1 \end{align*}

✓ Sympy. Time used: 0.638 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} e^{\frac {2 \sqrt {x^{3} + 1}}{3}} - 1 \]