23.3.119 problem 121

Internal problem ID [5833]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 121
Date solved : Tuesday, September 30, 2025 at 02:03:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to \frac {1}{2} e^{(x-1) x} \left (-2 e^x+c_2 e^{2 x}+2 c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*Derivative(y(x), x) + (4*x**2 - 3)*y(x) - exp(x**2) + 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) - 3*y(x) - exp(x**2) + Deriva