28.1.111 problem 134

Internal problem ID [4417]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 134
Date solved : Sunday, March 30, 2025 at 03:20:38 AM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y \left (x \,{\mathrm e}^{x^{2}}+y \sin \left (x \right ) \cos \left (x \right )\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 693

ode:=2*y(x)*(x*exp(x^2)+y(x)*sin(x)*cos(x))+(2*exp(x^2)+3*y(x)*sin(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 64.239 (sec). Leaf size: 628

ode=(2*y[x]*(x*Exp[x^2]+y[x]*Sin[x]*Cos[x]) )+(2*Exp[x^2]+3*y[x]*Sin[x]^2 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{12} \csc ^2(x) \left (4 e^{x^2}+\sqrt [3]{64 e^{3 x^2}+12 \sqrt {6} \sqrt {c_1 \sin ^4(x) \left (64 e^{3 x^2}-108 c_1 \cos (2 x)+27 c_1 \cos (4 x)+81 c_1\right )}-216 c_1 \cos (2 x)+54 c_1 \cos (4 x)+162 c_1}+\frac {16 e^{2 x^2}}{\sqrt [3]{64 e^{3 x^2}+12 \sqrt {6} \sqrt {c_1 \sin ^4(x) \left (64 e^{3 x^2}-108 c_1 \cos (2 x)+27 c_1 \cos (4 x)+81 c_1\right )}-216 c_1 \cos (2 x)+54 c_1 \cos (4 x)+162 c_1}}\right ) \\ y(x)\to -\frac {1}{24} \csc ^2(x) \left (8 e^{x^2}+i \left (\sqrt {3}+i\right ) \sqrt [3]{64 e^{3 x^2}+12 \sqrt {6} \sqrt {c_1 \sin ^4(x) \left (64 e^{3 x^2}-108 c_1 \cos (2 x)+27 c_1 \cos (4 x)+81 c_1\right )}-216 c_1 \cos (2 x)+54 c_1 \cos (4 x)+162 c_1}-\frac {16 i \left (\sqrt {3}-i\right ) e^{2 x^2}}{\sqrt [3]{64 e^{3 x^2}+12 \sqrt {6} \sqrt {c_1 \sin ^4(x) \left (64 e^{3 x^2}-108 c_1 \cos (2 x)+27 c_1 \cos (4 x)+81 c_1\right )}-216 c_1 \cos (2 x)+54 c_1 \cos (4 x)+162 c_1}}\right ) \\ y(x)\to -\frac {1}{24} \csc ^2(x) \left (8 e^{x^2}-i \left (\sqrt {3}-i\right ) \sqrt [3]{64 e^{3 x^2}+12 \sqrt {6} \sqrt {c_1 \sin ^4(x) \left (64 e^{3 x^2}-108 c_1 \cos (2 x)+27 c_1 \cos (4 x)+81 c_1\right )}-216 c_1 \cos (2 x)+54 c_1 \cos (4 x)+162 c_1}+\frac {16 i \left (\sqrt {3}+i\right ) e^{2 x^2}}{\sqrt [3]{64 e^{3 x^2}+12 \sqrt {6} \sqrt {c_1 \sin ^4(x) \left (64 e^{3 x^2}-108 c_1 \cos (2 x)+27 c_1 \cos (4 x)+81 c_1\right )}-216 c_1 \cos (2 x)+54 c_1 \cos (4 x)+162 c_1}}\right ) \\ \end{align*}

✗ Sympy

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

Timed Out