Question Number 74267 by smartsmith459@gmail.com last updated on 21/Nov/19
$$\mathrm{1}\:\:{what}\:{is}\:{the}\:{order}\:{and}\:{the}\:{degree}\:{of}\:{the}\:{differential}\:{equation} \\ $$$$\frac{{d}^{\mathrm{3}} {Z}}{{dt}^{\mathrm{3}} }\:+\left(\frac{{dZ}}{{dt}}\right)^{\mathrm{4}} \:−\:{y}^{\mathrm{5}} \:={e}^{−\mathrm{2}{x}} . \\ $$$$\left.\mathrm{2}\right)\:\:\mathrm{2}{x}\frac{{d}^{\mathrm{5}} {y}}{{dx}^{\mathrm{5}} }\:+\:\mathrm{5}{x}^{\mathrm{2}} \:\left(\frac{{dy}}{{dx}}\:\right)^{\mathrm{4}} \:−\:{xy}^{\mathrm{2}} \:=\:\mathrm{0}. \\ $$
Answered by liki last updated on 22/Nov/19
$$\:\:{soln}; \\ $$$$\:{Qn}\:\mathrm{1},\:{order}\:=\mathrm{3}\:{and}\:{degree}=\mathrm{1} \\ $$$$\:{Qn}\:\mathrm{2},\:{order}\:=\mathrm{5}\:{and}\:{degree}=\mathrm{1} \\ $$$$\:{Note}\::\: \\ $$$$\:{order}\:{look}\:{highest}\:{derivative}\: \\ $$$$\ast{degree}\:{check}\:{power}\:{of}\:{highest}\:{derivatives} \\ $$