83.36.11 problem 11

Internal problem ID [19445]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (A) at page 125
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 01:43:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve([(2*x^3-a)*diff(y(x),x$2)-6*x^2*diff(y(x),x)+6*x*y(x)=0,x],singsol=all)
 

\[ y \left (x \right ) = c_{1} x +c_{2} \left (x^{3}+a \right ) \]

✓ Solution by Mathematica

Time used: 0.437 (sec). Leaf size: 22

DSolve[(2*x^3-a)*D[y[x],{x,2}]-6*x^2*D[y[x],x]+6*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -a c_2-c_2 x^3+c_1 x \]