83.26.21 problem 21

Internal problem ID [19345]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 01:35:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve((5+2*x)^2*diff(y(x),x$2)-6*(5+2*x)*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} \left (\frac {5}{2}+x \right )^{2+\sqrt {2}}+c_{2} \left (\frac {5}{2}+x \right )^{2-\sqrt {2}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 40

DSolve[(5+2*x)^2*D[y[x],{x,2}]-6*(5+2*x)*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 (2 x+5)^{2+\sqrt {2}}+c_1 (2 x+5)^{2-\sqrt {2}} \]