Menu Close

1-what-is-the-order-and-the-degree-of-the-differential-equation-d-3-Z-dt-3-dZ-dt-4-y-5-e-2x-2-2x-d-5-y-dx-5-5x-2-dy-dx-4-xy-2-0-




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

Leave a Reply

Your email address will not be published. Required fields are marked *