83.25.2 problem 2

Internal problem ID [19322]
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 : 2
Date solved : Tuesday, January 28, 2025 at 01:34:06 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+7*x*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 24

DSolve[x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]+7*x*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \left (c_3 \log ^2(x)+c_2 \log (x)+c_1\right ) \]