73.14.9 problem 21.11

Internal problem ID [15419]
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 : Tuesday, January 28, 2025 at 07:55:06 AM
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*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

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

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