Home › Previous year questions › GATE 2019 BT › Question 48GATE 2019 BT – Question 48 Engineering Mathematics · Differential Equations: First order ODEs, higher order ODEs with constant coefficients, Cauchy and Euler equations, Laplace transforms · 2 marks · Multiple choice
Solve $dy/dx=x/y$ with y(0) = 1.
$x^2=y^2+1$ $y^2=x^2+1$ $y^2=2x^2+1$ $x^2-y^2=0$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (B) $y^2=x^2+1$
Explanation Separate variables: y dy = x dx. Integration gives y² = x²+C. The initial value y(0)=1 gives C=1, so B. The branch satisfying the initial condition is the positive root $y=\sqrt{x^2+1}$.
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