Assertion: Order of the differential equation whose solution is y = c 1 e x + c 2+ c 3 e x + c 4 is 4 . Reason: Order of the differential equation is equal to the number of independent arbitrary constant mentioned in the solution of differential equation.

Question

Assertion: Order of the differential equation whose solution is y = c 1 e x + c 2+ c 3 e x + c 4 is 4 . Reason: Order of the differential equation is equal to the number of independent arbitrary constant mentioned in the solution of differential equation. (A) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion. (B) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion (C) Assertion is correct, Reason is incorrect (D) Assertion is incorrect Reason is correct

Tardigrade Admin · Accepted Answer

∵ y=(c1 ec2+c3 ec4) ex=c ex (say) ∴ (d y/d x)=c ex=y ∴ Order is 1

Q. Assertion: Order of the differential equation whose solution is $y = c_{1} e^{x + c_{2}} + c_{3} e^{x + c_{4}}$ is $4.$
Reason: Order of the differential equation is equal to the number of independent arbitrary constant mentioned in the solution of differential equation.

Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.

Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion

Assertion is correct, Reason is incorrect

Assertion is incorrect Reason is correct

$∵ y = (c_{1} e^{c_{2}} + c_{3} e^{c_{4}}) e^{x} = c e^{x}$ (say)
$∴ \frac{d y}{d x} = c e^{x} = y$
$∴$ Order is 1

Q. Assertion: Order of the differential equation whose solution is y=c1​ex+c2​+c3​ex+c4​ is 4. Reason: Order of the differential equation is equal to the number of independent arbitrary constant mentioned in the solution of differential equation.