Example 20 - Chapter 9 Class 12 Differential Equations

Last updated at August 13, 2026 by

Example 20 - Find particular solution log (dy/dx) =3x + 4y - Examples

part 2 - Example 20 - Examples - Serial order wise - Chapter 9 Class 12 Differential Equations
part 3 - Example 20 - Examples - Serial order wise - Chapter 9 Class 12 Differential Equations

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Remove Ads
Teachoo ยท Class 12 Explore Class 12

Transcript

Example 20 Find the particular solution of the differential equation log(๐‘‘๐‘ฆ/๐‘‘๐‘ฅ)=3๐‘ฅ+4๐‘ฆ given that ๐‘ฆ=0 ๐‘คโ„Ž๐‘’๐‘› ๐‘ฅ=0 log(๐‘‘๐‘ฆ/๐‘‘๐‘ฅ)=3๐‘ฅ+4๐‘ฆ ๐’…๐’š/๐’…๐’™ = e(3x + 4y) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = e3x e4y Separating the variables ๐‘‘๐‘ฆ/๐‘’^4๐‘ฆ = e3x dx eโˆ’4y dy = e3x dx Integrating both sides โˆซ1โ–’ใ€–๐‘’^(โˆ’4๐‘ฆ) ๐‘‘๐‘ฆใ€—=โˆซ1โ–’๐‘’^3๐‘ฅ ๐‘‘๐‘ฅ ๐’†^(โˆ’๐Ÿ’๐’š)/(โˆ’๐Ÿ’)=๐’†^๐Ÿ‘๐’™/๐Ÿ‘+๐‘ช 0=๐‘’^3๐‘ฅ/3+๐‘’^(โˆ’4๐‘ฆ)/4+๐ถ ๐‘’^3๐‘ฅ/3 + ๐‘’^(โˆ’4๐‘ฆ)/4 + C = 0 (4๐‘’3๐‘ฅ" + " 3๐‘’^(โˆ’4๐‘ฆ))/12 + C = 0 (4๐‘’3๐‘ฅ" + " 3๐‘’^(โˆ’4๐‘ฆ) + 12๐ถ)/12 " = 0" ๐Ÿ’๐’†^๐Ÿ‘๐’™ + ๐Ÿ‘๐’†^(โˆ’๐Ÿ’๐’š) + 12C = 0 Given y = 0 when x = 0 Putting x = 0 & y = 0 in (1) 4๐‘’^(3(0)) + 3๐‘’^(โˆ’4(0)) + 12C = 0 4๐‘’^0 + 3๐‘’^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = โ€“ 7 C = (โˆ’๐Ÿ•)/๐Ÿ๐Ÿ Putting value of C in (1) 4๐‘’^3๐‘ฅ + 3๐‘’^(โˆ’4๐‘ฆ) + 12C = 0 4๐‘’^3๐‘ฅ + 3๐‘’^(โˆ’4๐‘ฆ) + 12((โˆ’7)/12) = 0 ๐Ÿ’๐’†^๐Ÿ‘๐’™ + ๐Ÿ‘๐’†^(โˆ’๐Ÿ’๐’š) โˆ’ 7 = 0

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.