83.24.5 problem 5

Internal problem ID [19319]
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 (A) at page 81
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:34:04 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)-6*y(x)=(ln(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\ln \left (x \right )^{2}}{6}-\frac {11 \ln \left (x \right )}{18}-\frac {85}{108}+c_3 \,x^{3}+c_{2} x^{2}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 38

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

\[ y(x)\to c_3 x^3+c_2 x^2+\frac {1}{108} \left (-18 \log ^2(x)-66 \log (x)-85\right )+c_1 x \]