12.20.7 problem section 9.4, problem 22

Internal problem ID [2228]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number : section 9.4, problem 22
Date solved : Monday, January 27, 2025 at 05:43:49 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=4 x \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=4\\ y^{\prime \prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 21

dsolve([x^3*diff(y(x),x$3)-2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-3*y(x)=4*x,y(1) = 4, D(y)(1) = 4, (D@@2)(y)(1) = 2],y(x), singsol=all)
 

\[ y = x \left (-\ln \left (x \right )^{2}+x^{2}-2 \ln \left (x \right )+3\right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 22

DSolve[{x^3*D[y[x],{x,3}]-2*x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-3*y[x]==4*x,{y[1]==4,Derivative[1][y][1]==4,Derivative[2][y][1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (x^2-\log ^2(x)-2 \log (x)+3\right ) \]