Differential Equations

Easymathematics

The solution of the differential equation $d y / d x + y / x = x^{2}$ is:

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$y = x^{3} /4 + C / x$

$y = x^{3} /3 + C / x$

$y = x^{2} /4 + C$

$y = x^{4} /4 + C / x$

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About This Question

Subject: mathematics
Chapter: differential equations
Topic: differential equations
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

$y = x^{3} /4 + C / x$

Identify the form: This is a Linear Differential Equation of the form $d y / d x + P (x) y = Q (x)$ . $P (x) = 1/ x, Q (x) = x^{2}$ .
Find Integrating Factor (IF): IF $= e^{\int (1/ x) d x} = e^{l n x} = x$ .
Solution formula: $y \cdot IF = \int (Q \cdot IF) d x + C$ $x y = \int (x^{2} \cdot x) d x + C$ $x y = \int x^{3} d x + C$ $x y = x^{4} /4 + C$
Isolate $y$ : $y = x^{3} /4 + C / x$ .

This easy difficulty mathematics question is from the chapter differential equations, covering the topic of differential equations. It appeared in the 2025 exam.

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Differential Equations

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More differential equations Practice Questions

Let $f (x)$ be differentiable s.t. $f^{'} (x) = 2 - f (x) / x$ and $f (1) = 1$ . Then $f (x)$ is:

The differential equation of the family of parabolas $y^{2} = 4 a (x + a)$ is:

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Solution

Differential Equations

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Solution

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More differential equations Practice Questions

Let f(x) be differentiable s.t. f′(x)=2−f(x)/x and f(1)=1. Then f(x) is:

The differential equation of the family of parabolas y2=4a(x+a) is:

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Solution

Let $f (x)$ be differentiable s.t. $f^{'} (x) = 2 - f (x) / x$ and $f (1) = 1$ . Then $f (x)$ is:

The differential equation of the family of parabolas $y^{2} = 4 a (x + a)$ is: