The order of the differential equation whose | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The given general solution is $y = a_1(a_2 + a_3) \cdot \cos(x + a_4) - a_5 e^{x + a_6}$.Let $C_1 = a_1(a_2 + a_3)$,$C_2 = a_4$,and $C_3 = a_5$,$C

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) The given general solution is $y = a_1(a_2 + a_3) \cdot \cos(x + a_4) - a_5 e^{x + a_6}$.Let $C_1 = a_1(a_2 + a_3)$,$C_2 = a_4$,and $C_3 = a_5$,$C_4 = a_6$.Then the equation can be rewritten as $y = C_1 \cos(x + C_2) - C_3 e^{x + C_4}$.Using the trigonometric identity $\cos(x + C_2) = \cos x \cos C_2 - \sin x \sin C_2$,we get:$y = C_1(\cos x \cos C_2 - \sin x \sin C_2) - C_3 e^{x + C_4}$.$y = (C_1 \cos C_2) \cos x - (C_1 \sin C_2) \sin x - (C_3 e^{C_4}) e^x$.Let $A = C_1 \cos C_2$,$B = -C_1 \sin C_2$,and $D = -C_3 e^{C_4}$.Thus,the equation simplifies to $y = A \cos x + B \sin x + D e^x$.There are $3$ independent arbitrary constants $(A, B, D)$.The order of a differential equation is equal to the number of independent arbitrary constants in its general solution.Therefore,the order of the differential equation is $3$.

The order of the differential equation whose general solution is $y = a_1(a_2 + a_3) \cdot \cos(x + a_4) - a_5 e^{x + a_6}$ is . . . . . . .

Similar Questions

For the differential equation $\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^2}$, find the order and degree.

The order and degree of the differential equation $\left[1+\frac{1}{(\frac{dy}{dx})^{2}}\right]^{\frac{5}{3}}=5 \frac{d^{2}y}{dx^{2}}$ are respectively:

Which of the following is a second-order differential equation?

The order and degree of the differential equation $(\frac{d^3y}{dx^3})^{2/3} - 3 \frac{d^2y}{dx^2} + 5 \frac{dy}{dx} + 4 = 0$ are respectively:

The family of curves $y = Ax + A^3$ is represented by a differential equation of degree:

Vedclass Test Series

Exam Paper Generator

Online Exam Module