82.39.7 problem Ex. 7

Internal problem ID [18939]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 7
Date solved : Tuesday, January 28, 2025 at 08:29:23 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y&=x^{2}+4 x +3 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 48

dsolve(16*(x+1)^4*diff(y(x),x$4)+96*(x+1)^3*diff(y(x),x$3)+104*(x+1)^2*diff(y(x),x$2)+8*(x+1)*diff(y(x),x)+y(x)=x^2+4*x+3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x^{2}+52 x +51\right ) \sqrt {x +1}+225 \left (c_4 x +c_3 +c_4 \right ) \ln \left (x +1\right )+225 c_{2} x +225 c_{1} +225 c_{2}}{225 \sqrt {x +1}} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 61

DSolve[16*(x+1)^4*D[y[x],{x,4}]+96*(x+1)^3*D[y[x],{x,3}]+104*(x+1)^2*D[y[x],{x,2}]+8*(x+1)*D[y[x],x]+y[x]==x^2+4*x+3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{225} \left (x^2+52 x+\frac {225 c_1}{\sqrt {x+1}}+225 c_3 \sqrt {x+1}+51\right )+\frac {(c_4 (x+1)+c_2) \log (x+1)}{\sqrt {x+1}} \]