73.14.9 problem 21.11

Internal problem ID [15348]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.11
Date solved : Monday, March 31, 2025 at 01:35:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=10 x +12 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=6\\ y^{\prime }\left (1\right )&=8 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 10*x+12; 
ic:=y(1) = 6, D(y)(1) = 8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 5 x^{3}-6 x^{2}+5 x +2 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 20

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==10*x+12; 
ic={y[1]==6,Derivative[1][y][1]==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 5 x^3-6 x^2+5 x+2 \]

✓ Sympy. Time used: 0.348 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) - 10*x + 6*y(x) - 12,0) 
ics = {y(1): 6, Subs(Derivative(y(x), x), x, 1): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 x^{3} - 6 x^{2} + 5 x + 2 \]