Q.3 obtain the orthogonal trajectory of the family of the following curves 1.y- 2. y-c sin r. 3. (r-2)+ (y- 1)*- c 4. y-e 5. y +c. 6. -r"(1- cr).

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here is question 2...

this is the solution....

you first find Dy/dx and from this equation and given equation remove c. which gives you differential equation. and then in this DE replace Dy/dx by - dx/dy, which gives DE of orth...