77.1.146 problem 172 (page 245)

Internal problem ID [17965]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 172 (page 245)
Date solved : Monday, March 31, 2025 at 04:52:42 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 23

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

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

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (4*x**2*y(x) - y(x) + 3*exp(x**2)*sin(2*x) + Derivative(y(x), (x, 2)))/(4*x) cannot be solved by the factorable group method