83.49.18 problem Ex 18 page 133

Internal problem ID [19631]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 18 page 133
Date solved : Tuesday, January 28, 2025 at 02:05:32 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y&=4 \cos \left (\ln \left (1+x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve((1+x)^2*diff(y(x),x$2)+(1+x)*diff(y(x),x)+y(x)=4*cos(ln(1+x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{2} +2 \ln \left (x +1\right )\right ) \sin \left (\ln \left (x +1\right )\right )+\cos \left (\ln \left (x +1\right )\right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 31

DSolve[(1+x)^2*D[y[x],{x,2}]+(1+x)*D[y[x],x]+y[x]==4*Cos[Log[1+x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (1+c_1) \cos (\log (x+1))+(2 \log (x+1)+c_2) \sin (\log (x+1)) \]