The GATE Grind

GATE 2020 IN – Question 37

Engineering Mathematics · Differential equations: First order and second order linear equations with constant coefficients, variation of parameters, Cauchy's and Euler's equations, initial and boundary value problems, partial differential equations by variable separable method · 2 marks · Multiple choice

The ODE is $dx/dt=\sin x$, with x(0) = 0. Its solution is

  1. $x(t)=0$
  2. $x(t)=\sin t$
  3. $x(t)=\cos t$
  4. $x(t)=\sin t-\cos t$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $x(t)=0$

Explanation

The constant solution x(t) = 0 has derivative zero and right side sin 0 = 0, and satisfies the initial condition. Since sin x is continuously differentiable and globally Lipschitz, the initial-value solution is unique. Thus A; a nonconstant sinusoid does not solve the nonlinear ODE.

More Differential equations: First order and second order linear equations with constant coefficients, variation of parameters, Cauchy's and Euler's equations, initial and boundary value problems, partial differential equations by variable separable method questions

All Differential equations: First order and second order linear equations with constant coefficients, variation of parameters, Cauchy's and Euler's equations, initial and boundary value problems, partial differential equations by variable separable method questions →