75.20.23 problem 662

Internal problem ID [17086]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 662
Date solved : Monday, March 31, 2025 at 03:40:21 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=x*diff(diff(y(x),x),x)-(2*x^2+1)*diff(y(x),x) = 4*x^3*exp(x^2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 x^{2}+c_1 -2\right ) {\mathrm e}^{x^{2}}}{2}+c_2 \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 25

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

\[ y(x)\to e^{x^2} \left (x^2-1+\frac {c_1}{2}\right )+c_2 \]

✓ Sympy. Time used: 141.303 (sec). Leaf size: 930

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

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