Quiz

Generating...

quiz04_n14

Solve the second-order linear ODE $\displaystyle \left(2\,x+1\right)\,\left({{d^2}\over{d\,x^2}}\,y\right)+4\,x\, \left({{d}\over{d\,x}}\,y\right)-4\,y=0$ using a first solution $\displaystyle y_{1}=x$ .
$\displaystyle y=c_{2}\,e^{2\,x}+c_{1}\,x$ $\displaystyle y=c_{2}\,e^ {- x }+c_{1}\,x$ $\displaystyle y=c_{2}\,e^{x}+c_{1}\,x$ $\displaystyle y=c_{2}\,e^ {- 2\,x }+c_{1}\,x$
Solve the second-order linear ODE $\displaystyle {{d^2}\over{d\,x^2}}\,y+3\,\left({{d}\over{d\,x}}\,y\right)+2\,y=0$ .
$\displaystyle y=c_{1}\,e^{{{\left(\sqrt{17}-3\right)\,x}\over{2}}}+c_{2}\,e^{{{ \left(-\sqrt{17}-3\right)\,x}\over{2}}}$ $\displaystyle y=c_{1}\,e^ {- x }+c_{2}\,e^ {- 2\,x }$ $\displaystyle y=e^ {- {{x}\over{2}} }\,\left(c_{1}\,\sin \left({{\sqrt{7}\,x }\over{2}}\right)+c_{2}\,\cos \left({{\sqrt{7}\,x}\over{2}}\right) \right)$ $\displaystyle y=c_{1}\,e^{x}+c_{2}\,e^ {- 2\,x }$
Solve the second-order linear ODE $\displaystyle {{d^2}\over{d\,x^2}}\,y-2\,\left({{d}\over{d\,x}}\,y\right)+2\,y=0$ subject to y(0) = 3 and y'(0) = 5 .
$\displaystyle y=2\,e^ {- x }\,\sin x+3\,e^ {- x }\,\cos x$ $\displaystyle y=2\,e^{x}\,\sin x+3\,e^{x}\,\cos x$ $\displaystyle y=3\,e^ {- x }\,\sin x+2\,e^ {- x }\,\cos x$ $\displaystyle y=3\,e^{x}\,\sin x+2\,e^{x}\,\cos x$
Solve the second-order linear ODE $\displaystyle x^2\,\left({{d^2}\over{d\,x^2}}\,y\right)+x\,\left({{d}\over{d\,x}} \,y\right)-16\,y=0$ using a known solution $\displaystyle y_{1}=x^4$ .
$\displaystyle y=c_{1}\,x^4+{{c_{2}}\over{x^7}}$ $\displaystyle y=c_{1}\,x^4+{{c_{2}}\over{x^4}}$ $\displaystyle y=c_{2}\,x^4-{{c_{1}}\over{4}}$ $\displaystyle y=c_{1}\,x^4+c_{2}\,x$
Solve the second-order linear ODE $\displaystyle {{d^2}\over{d\,x^2}}\,y-3\,\left({{d}\over{d\,x}}\,y\right)+2\,y=0$ .
$\displaystyle y=c_{1}\,e^{2\,x}+c_{2}\,e^{x}$ $\displaystyle y=c_{1}\,e^ {- x }+c_{2}\,e^ {- 2\,x }$ $\displaystyle y=c_{1}\,e^{x}+c_{2}\,e^ {- x }$ $\displaystyle y=c_{1}\,e^{2\,x}+c_{2}\,e^ {- 2\,x }$

Department of Mathematics
Last modified: 2026-02-06