83.12.3 problem 3

Internal problem ID [19096]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (D) at page 37
Problem number : 3
Date solved : Thursday, March 13, 2025 at 01:40:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=15 x^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)-15*y(x) = 15*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = -\left (\left (x^{2}+\frac {4}{15} x +\frac {38}{225}\right ) {\mathrm e}^{5 x}-{\mathrm e}^{8 x} c_{2} -c_{1} \right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 35

ode=D[y[x],{x,2}]+2*D[y[x],x]-15*y[x]==15*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -x^2-\frac {4 x}{15}+c_1 e^{-5 x}+c_2 e^{3 x}-\frac {38}{225} \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-15*x**2 - 15*y(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{3 x} - x^{2} - \frac {4 x}{15} - \frac {38}{225} \]