$y=e^{2 x}(a+b x)$
$y=e^{2 x}(a+b x)$ ...(1)
Differentiating both sides with respect to x, we get:
$y^{\prime}=2 e^{2 x}(a+b x)+e^{2 x} \cdot b$
$\Rightarrow y^{\prime}=e^{2 x}(2 a+2 b x+b)$ ...(2)
Multiplying equation (1) with 2 and then subtracting it from equation (2), we get:
$y^{\prime}-2 y=e^{2 x}(2 a+2 b x+b)-e^{2 x}(2 a+2 b x)$
$\Rightarrow y^{\prime}-2 y=b e^{2 x}$ ...(3)
Differentiating both sides with respect to x, we get:
$y^{\prime \prime}-2 y^{\prime}=2 b e^{2 x}$ (4)
Dividing equation (4) by equation (3), we get:
$\frac{y^{\prime \prime}-2 y^{\prime}}{y^{\prime}-2 y}=2$
$\Rightarrow y^{\prime \prime}-2 y^{\prime}=2 y^{\prime}-4 y$
$\Rightarrow y^{\prime \prime}-4 y^{\prime}+4 y=0$
This is the required differential equation of the given curve.
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- Current Electricity
- Thermoelectric Effects of Electric Current
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All Study Material
- 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,