The GATE Grind

GATE 2018 ME (ME2) – Question 14

Engineering Mathematics · Differential Equations: First order and higher order linear equations, Euler-Cauchy equation · 1 mark · Multiple choice

If $y^3\frac{dy}{dx}+x^3=0$ with $y(0)=1$, find $y(-1)$.

  1. −2
  2. −1
  3. 0
  4. 1

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 0

Explanation

Separate variables: $y^3\,dy=-x^3\,dx$. Integration gives $y^4+x^4=C$. Since $y(0)=1$, C = 1. At x = −1, $y^4=0$, hence **y = 0, C**.