Question

Solve dy/dx-tan(y-x)=1 please can you solve this question.

Answer 1

Answer:

Make a substitution to form a new and simpler differential equation:  

dy / dx - tan(y - x) = 1  

dy / dx = 1 + tan(y - x)  

Let u = y - x,  

y = u + x  

dy / dx = du / dx + 1  

du / dx + 1 = 1 + tanu  

Solve this differential equation by separating the variables then integrating:  

du / dx = tanu  

du / tanu du = dx  

cotu du = dx  

∫ cotu du = ∫ 1 dx  

ln|sinu| = x + C  

sinu = ℮^(x + C)  

sinu = ℮ᶜ℮˟  

sinu = C℮˟  

u = sinˉ¹(C℮˟)  

Find the general solution by substituting back for the previous variables:  

Since u = y - x,  

y - x = sinˉ¹(C℮˟)  

y = x + sinˉ¹(C℮˟)