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Index  Inference Rule  Input latex  Feeds latex  Output latex  step validity  dimension check  unit check  notes 

3  declare initial expr 



no validation is available for declarations 
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7  declare guess solution 



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8991236357:
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8991236357:
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what, when differentiated twice, yields a negative of itself? cosine 
10  LHS of expr 1 equals LHS of expr 2 



input diff is d**2*(pdg4037 + x)/dt**2 diff is k*x/pdg5156 + pdg2321**2*pdg9885*cos(pdg1467*pdg2321) diff is A*pdg2321**2*cos(pdg2321*pdg9491) + pdg1356*pdg4037/pdg5156 
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8991236357: 1772973171: 
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8991236357: 1772973171: 

11  substitute LHS of expr 1 into expr 2 



LHS diff is k*(A*cos(pdg2321*pdg9491)  x)/pdg5156 RHS diff is 0 
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1772973171: 2148049269: 
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1772973171: 2148049269: 

13  square root both sides 



no check performed 
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1784114349: 1888494137: 
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1784114349: 1888494137: 

1  declare initial expr 



no validation is available for declarations 
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5345738321:


2  declare initial expr 



no validation is available for declarations 
4428528271:

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6  LHS of expr 1 equals LHS of expr 2 



input diff is a + pdg9140 diff is d**2*pdg4037/dt**2 + pdg1356*pdg4037/pdg5156 diff is d**2*x/dt**2  pdg1356*pdg4037/pdg5156 
8655294002:
6831694380: 8991236357: 
8655294002:
6831694380: 8991236357: 

4  LHS of expr 1 equals LHS of expr 2 



input diff is pdg4183 + pdg4202 diff is 0 diff is 0 
5345738321:
4428528271: 2334518266: 
5345738321:
4428528271: 2334518266: 

12  multiply both sides by 



LHS diff is (A*k*pdg1467*cos(pdg2321*pdg9491) + pdg1356)/pdg5156 RHS diff is pdg2321**2*(A*pdg1467*cos(pdg2321*pdg9491) + 1) 
2148049269:
1931103031: 
2148049269:
1931103031: 

9  differentiate with respect to 



no check performed 
7652131521:
5945893986: 
7652131521:
5945893986: 

5  divide both sides by 



valid 
2334518266:
8655294002: 
2334518266:
8655294002: 

8  differentiate with respect to 



no check performed 
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7652131521: 
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14  substitute RHS of expr 1 into expr 2 



LHS diff is 0 RHS diff is pdg9885*(cos(pdg1467*sqrt(pdg1356/pdg5156))  cos(k*pdg1467/pdg5156)) 
1784114349:
5415824175: 6908055431: error for dim with 6908055431 
1784114349:
5415824175: 6908055431: N/A 

15  declare final expr 



no validation is available for declarations 
6908055431:
error for dim with 6908055431 
6908055431:
N/A 