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The order of the differential equation whosegeneral solution is given by `y=(C_1+C_2)cos(x+C_3)-C_4e^(x+4_5),`where `C_1,C_2,C_3,C_4,C_5`, are arbitrary constants, is(a)5(b) 4 (c)3 (d) 2A. (a) 5B. (b) 4C. (c) 3D. (d) 2 |
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Answer» Correct Answer - (c) Given, `y=(c_(1)+c_(2))cos (x+c_(3))-c_(4)e^(x+c_(5)) …. (i)` ` rArr y=(c_(1)+c_(2))cos (x+c_(3))-c_(4)e^(x)cdot e^(c_(5)) ` Now, let `c_(1)+c_(2)=A,c_(3)=B,c_(4)e^(c_(5))=c` `rArr y=A cos (x+B)-ce^(x) …(ii)` On differentiating w.r.t.x, we get `dy/dx=-A sin (A+B)-ce^(x) …(iii)` Again, on differentiating w.r.t.x, we get `(d^(2)y)/dx^(2)=-Acos (x+B)-ce^(x) … (iv)` `rArr (d^(2)y)/dx^(2)=-y-2ce^(x) … (v)` `rArr (d^(2)y)/dx^(2)+y=-2ce^(x)` Again, on differentiating w.r.t.x, we get ` (d^(3)y)/dx^(2)+dy/dx=-2ce^(x) ..(vi)` `rArr (d^(3)y)/dx^(2)+dy/dx=(d^(2)y)/dx^(2)+y [from Eq. (v)]` which is a differential equation of order 3. |
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