PYQs Based Test - 14 : Euler-Cauchy Equations

Topics Covered

Sample Questions from this Test

1. General solution of $x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}-y=0$ is
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2. Consider the differential equation $x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}-4y=0$ with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is
3. The solution of differential equation $x^2\frac{d^{2}y}{d{x}^2}-2x\frac{dy}{dx}+2y=0$ will be ___________, where c₁ and c₂ are arbitrary constants.

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Test Instructions

• The test contains 10 questions and a total of 16 marks.
• You will have 180 minutes to complete the test. The timer cannot be paused once started.
• Negative marking: 0.25 mark(s) deducted per wrong answer.
• Use the question palette to mark questions for review and navigate freely.
• Detailed solutions and analytics are available immediately after submission.
• This is a free practice test. No login required to attempt.