83.25.1 problem 1

Internal problem ID [19321]
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 (B) at page 83
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:34:05 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-4 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(x^2*diff(y(x),x$3)+x*diff(y(x),x$2)-4*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +c_{2} x^{3}+\frac {c_3}{x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

DSolve[x^2*D[y[x],{x,3}]+x*D[y[x],{x,2}]-4*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^3}{3}-\frac {c_1}{x}+c_3 \]