75.16.7 problem 480

Internal problem ID [16909]
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 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 480
Date solved : Monday, March 31, 2025 at 03:35:14 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

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

\[ y = \frac {\left (9 x^{2}+72 c_1 -24 x +32\right ) {\mathrm e}^{\frac {3 x}{4}}}{54}+c_2 \]

✓ Mathematica. Time used: 4.638 (sec). Leaf size: 44

ode=D[y[x],{x,2}]-3*D[y[x],x]==x*Exp[3/4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^xe^{3 K[2]} \left (c_1+\int _1^{K[2]}e^{-\frac {9 K[1]}{4}} K[1]dK[1]\right )dK[2]+c_2 \]

✓ Sympy. Time used: 0.230 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} + \left (C_{2} + \frac {x^{2}}{6} - \frac {4 x}{9}\right ) e^{\frac {3 x}{4}} \]