40.12.5 problem 10

Internal problem ID [6753]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre). Supplemetary problems. Page 110
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:27:31 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y&=\ln \left (1+x \right )^{2}+x -1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 53

dsolve((x+1)^2*diff(y(x),x$2)+(x+1)*diff(y(x),x)-y(x)=(ln(x+1))^2+x-1,y(x), singsol=all)
 

\[ y = \frac {\left (-4 x -4\right ) \ln \left (x +1\right )^{2}+2 \left (x +1\right )^{2} \ln \left (x +1\right )+4 c_2 \,x^{2}+8 c_2 x +4 c_1 +4 c_2 -3}{4 x +4} \]

✓ Solution by Mathematica

Time used: 0.336 (sec). Leaf size: 72

DSolve[(x+1)^2*D[y[x],{x,2}]+(x+1)*D[y[x],x]-y[x]==(Log[x+1])^2+x-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(-1+2 c_1+2 i c_2) x^2-4 (x+1) \log ^2(x+1)+2 (x+1)^2 \log (x+1)+(-2+4 c_1+4 i c_2) x-1+4 c_1}{4 (x+1)} \]