Question:
$x^{5} \frac{d y}{d x}=-y^{5}$
Solution:
The given differential equation is:
$x^{5} \frac{d y}{d x}=-y^{5}$
$\Rightarrow \frac{d y}{y^{5}}=-\frac{d x}{x^{5}}$
$\Rightarrow \frac{d x}{x^{5}}+\frac{d y}{y^{5}}=0$
Integrating both sides, we get:
$\int \frac{d x}{x^{5}}+\int \frac{d y}{y^{5}}=k \quad$ (where $k$ is any constant)
$\Rightarrow \int x^{-5} d x+\int y^{-5} d y=k$
$\Rightarrow \frac{x^{-4}}{-4}+\frac{y^{-4}}{-4}=k$
$\Rightarrow x^{-4}+y^{-4}=-4 k$
$\Rightarrow x^{-4}+y^{-4}=\mathrm{C}$ $(\mathrm{C}=-4 k)$
This is the required general solution of the given differential equation.
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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