2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Differential Equations

JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The order of the differential equation whose general solution is given by \[y={{C}_{1}}{{e}^{2x+{{C}_{2}}}}+\] \[{{C}_{3}}{{e}^{x}}+{{C}_{4}}\sin (x+{{C}_{5}})\]  is [AMU 2000]

    A) 5    

    B) 4

    C) 3    

    D) 2

    Correct Answer: B

    Solution :

    • \[y={{C}_{1}}{{e}^{2x+{{C}_{2}}}}+{{C}_{3}}{{e}^{x}}+{{C}_{4}}\sin (x+{{C}_{5}})\]          
    • \[={{C}_{1}}.{{e}^{{{C}_{2}}}}{{e}^{2x}}+{{C}_{3}}{{e}^{x}}+{{C}_{4}}(\sin x\cos {{C}_{5}}+\cos x\sin {{C}_{5}})\]        
    • \[=A{{e}^{2x}}+{{C}_{3}}{{e}^{x}}+B\sin x+D\cos x\]        
    • Here, \[A={{C}_{1}}{{e}^{{{C}_{2}}}}\], \[B={{C}_{4}}\cos {{C}_{5}}\], \[D={{C}_{4}}\sin {{C}_{5}}\]        
    • (Since equation consists of four arbitrary constants) \ order of differential equation = 4.


You need to login to perform this action.
You will be redirected in 3 sec spinner