Solving Linear Differential Equations of First Order
If y1 x is a ...
Question
If y1(x) is a solution of the differential equation dydx+f(x)y=0, then a solution of differential equation dydx+f(x)y=r(x) is
A
1y(x)∫y1(x)dx
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
y1(x)∫r(x)y1(x)dx+c
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
intr(x)y1(x)dx
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
noneofthese
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is By1(x)∫r(x)y1(x)dx+c i)dydx+f(x)y1=0⇒f(x)=−1y1dy1dxii)dydx−1y1dy1dx.y=r(x)e−∫1y1dydxdx=e−∫dy1dx=1y1ddx(yy1)=r(x)y1⇒yy1=∫r(x)dx+cy1y=y1∫r(x)dxy1+cy1